scholarly journals Computing Birational Polynomial Surface Parametrizations without Base Points

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2224
Author(s):  
Sonia Pérez-Díaz ◽  
Juan Rafael Sendra
Keyword(s):  
Transversality Condition ◽  
Base Points ◽  
Polynomial Surface

In this paper, we present an algorithm for reparametrizing birational surface parametrizations into birational polynomial surface parametrizations without base points, if they exist. For this purpose, we impose a transversality condition to the base points of the input parametrization.

ANALISIS PENGEMBANGAN KLASTER HORTIKULTURA DI KABUPATEN NGAWI

2018 ◽  
Vol 16 (1) ◽  
pp. 103-117
Author(s):  
Nurul Istiqomah ◽  
Nunung Sri Mulyani ◽  
Izza Mafruhah ◽  
Dewi Ismoyowati
Keyword(s):  
Fruits And Vegetables ◽  
Agricultural Sector ◽  
Free Market ◽  
Descriptive Analysis ◽  
Free Trade Area ◽  
Government Support ◽  
Buffer Zones ◽  
Horticultural Crops ◽  
Base Points ◽  
Vegetables And Fruits

Indonesia as an agricultural country has the potential to compete in the agricultural market in the international market, in line with the existence of the ASEAN / ASEAN Free Trade Area (AFTA) Free Market. Ngawi Regency is a fertile area and is one of the buffer zones of the agricultural sector in East Java. Horticulture commodities are one of the main sources in the agricultural sector, because they have high potential and can contribute to the economy of a region. Horticultural commodities in the form of fruits and vegetables are an important food source to meet the nutritional needs of the community. Agriculture with a focus on horticultural crops in Ngawi Regency was developed with a cluster system based on the level of progress, harvest area and by considering agro-climate to map the superior horticultural commodities. The purpose of this study was to map the conditions of horticultural agriculture and analyze problems in the cluster of horticulture plants in Ngawi Regency. The research method is a mixed method using descriptive analysis, Geographic Information System (GIS), and using the Analysis Hierarchy Process (AHP). The conclusion of this study is that the potential development of horticultural clusters in Ngawi Regency requires structuring and developing the location of base commodities in accordance with the conditions of the agro-ecosystem. The development of existing commodities at these base points will make the commodity superior and support the creation of horticultural cluster centers and the development of existing agribusiness in an area. Development of horticulture base commodities for seasonal vegetables and fruits can be adjusted to the LQ results for each sub-district in Ngawi Regency. The results of the Indepth interview processed using AHP obtained results that in fact there were three main factors in the development of clusters, namely production consisting of four derivative factors namely research and development, superior seeds, fertilizers and anti-pest drugs and then marketing with derivative factors namely product standardization, packaging , traditional markets and modern markets. Then the third factor of the institution consists of training, networking, government support and assistance. 

scholarly journals Self-Localization of Mobile Robots Using a Single Catadioptric Camera with Line Feature Extraction

Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4719
Author(s):  
Huei-Yung Lin ◽  
Yuan-Chi Chung ◽  
Ming-Liang Wang
Keyword(s):  
Mobile Robots ◽  
Ground Plane ◽  
Feature Correspondence ◽  
Projection Model ◽  
3D Space ◽  
Base Points ◽  
Real Scene ◽  
Correspondence Matching ◽  
Mobile Robot Localization ◽  
Catadioptric Camera

This paper presents a novel self-localization technique for mobile robots using a central catadioptric camera. A unified sphere model for the image projection is derived by the catadioptric camera calibration. The geometric property of the camera projection model is utilized to obtain the intersections of the vertical lines and ground plane in the scene. Different from the conventional stereo vision techniques, the feature points are projected onto a known planar surface, and the plane equation is used for depth computation. The 3D coordinates of the base points on the ground are calculated using the consecutive image frames. The derivation of motion trajectory is then carried out based on the computation of rotation and translation between the robot positions. We develop an algorithm for feature correspondence matching based on the invariability of the structure in the 3D space. The experimental results obtained using the real scene images have demonstrated the feasibility of the proposed method for mobile robot localization applications.

scholarly journals Manin Involutions for Elliptic Pencils and Discrete Integrable Systems

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Matteo Petrera ◽  
Yuri B. Suris ◽  
Kangning Wei ◽  
René Zander
Keyword(s):  
Integrable Systems ◽  
Geometric Description ◽  
Discrete Integrable Systems ◽  
Birational Maps ◽  
Base Points ◽  
Special Geometry ◽  
Low Degree ◽  
Geometric Study

AbstractWe contribute to the algebraic-geometric study of discrete integrable systems generated by planar birational maps: (a) we find geometric description of Manin involutions for elliptic pencils consisting of curves of higher degree, birationally equivalent to cubic pencils (Halphen pencils of index 1), and (b) we characterize special geometry of base points ensuring that certain compositions of Manin involutions are integrable maps of low degree (quadratic Cremona maps). In particular, we identify some integrable Kahan discretizations as compositions of Manin involutions for elliptic pencils of higher degree.

scholarly journals A plane quartic curve with twelve undulations

1945 ◽  
Vol 35 ◽  
pp. 10-13 ◽  
Author(s):  
W. L. Edge
Keyword(s):  
Homogeneous Coordinates ◽  
Quartic Curve ◽  
Base Points ◽  
Octahedral Group ◽  
Quartic Form ◽  
Image Position ◽  
Quartic Curves ◽  
Set Of Points

The pencil of quartic curveswhere x, y, z are homogeneous coordinates in a plane, was encountered by Ciani [Palermo Rendiconli, Vol. 13, 1899] in his search for plane quartic curves that were invariant under harmonic inversions. If x, y, z undergo any permutation the ternary quartic form on the left of (1) is not altered; nor is it altered if any, or all, of x, y, z be multiplied by −1. There thus arises an octahedral group G of ternary collineations for which every curve of the pencil is invariant.Since (1) may also be writtenthe four linesare, as Ciani pointed out, bitangents, at their intersections with the conic C whose equation is x2 + y2 + z2 = 0, to every quartic of the pencil. The 16 base points of the pencil are thus all accounted for—they consist of these eight contacts counted twice—and this set of points must of course be invariant under G. Indeed the 4! collineations of G are precisely those which give rise to the different permutations of the four lines (2), a collineation in a plane being determined when any four non-concurrent lines and the four lines which are to correspond to them are given. The quadrilateral formed by the lines (2) will be called q.

Application of Combination Evaluation for Academic Title Evaluation

2011 ◽  
Vol 50-51 ◽  
pp. 756-760
Author(s):  
Bao Feng Li ◽  
Jing Guo Qu ◽  
Pu Yu Hao
Keyword(s):  
Associate Professor ◽  
Topsis Method ◽  
Entropy Weight ◽  
Base Points ◽  
Subjective Weight ◽  
Evaluation Models ◽  
Entropy Weight Method ◽  
Weight Method ◽  
Double Base

In this paper, using the relevant data of 34 teaching staffs who participate in the academic title evaluation of associate professor in 2010, firstly it introduces the entropy weight method, Topsis method with subjective weight, Topsis method with objective weight and double base points method with subjective weight to evaluate and sort the performance of 34 teaching staffs. Secondly, two combination evaluation models are constructed to do the same work and the conclusions are more science and rational.

Transformations depending on sets of associated points

1952 ◽  
Vol 48 (3) ◽  
pp. 383-391
Author(s):  
T. G. Room
Keyword(s):  
Projective Space ◽  
Projective Plane ◽  
Three Dimensional ◽  
Cubic Curves ◽  
Birational Transformations ◽  
Quadric Surfaces ◽  
Base Points ◽  
Dimensional Projective Space ◽  
Quartic Curves

This paper falls into three sections: (1) a system of birational transformations of the projective plane determined by plane cubic curves of a pencil (with nine associated base points), (2) some one-many transformations determined by the pencil, and (3) a system of birational transformations of three-dimensional projective space determined by the elliptic quartic curves through eight associated points (base of a net of quadric surfaces).

scholarly journals K-RATIONAL D-BRANE CRYSTALS

2012 ◽  
Vol 27 (22) ◽  
pp. 1250112
Author(s):  
ROLF SCHIMMRIGK
Keyword(s):  
String Theory ◽  
Algebraic Number ◽  
Special Class ◽  
Building Blocks ◽  
Number Fields ◽  
Central Point ◽  
Algebraic Number Fields ◽  
Special Values ◽  
Toroidal Compactifications ◽  
Base Points

In this paper the problem of constructing space–time from string theory is addressed in the context of D-brane physics. It is suggested that the knowledge of discrete configurations of D-branes is sufficient to reconstruct the motivic building blocks of certain Calabi–Yau varieties. The collections of D-branes involved have algebraic base points, leading to the notion of K-arithmetic D-crystals for algebraic number fields K. This idea can be tested for D0-branes in the framework of toroidal compactifications via the conjectures of Birch and Swinnerton-Dyer. For the special class of D0-crystals of Heegner type these conjectures can be interpreted as formulae that relate the canonical Néron–Tate height of the base points of the D-crystals to special values of the motivic L-function at the central point. In simple cases the knowledge of the D-crystals of Heegner type suffices to uniquely determine the geometry.

Structural Analysis by the Differential Quadrature Method Using Modified Weighting Matrices

1998 ◽  
Author(s):  
Siu-Tong Choi ◽  
Yu-Tuan Chou
Keyword(s):  
Boundary Conditions ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Sampling Point ◽  
Order Partial Differential Equation ◽  
Quadrature Method ◽  
The Finite Element Method ◽  
Computationally Efficient ◽  
Base Points ◽  
Sampling Points

Abstract The differential quadrature method has lately been more and more often used for analysis of engineering problems as an alternative for the finite element method or finite difference method. In this paper, static, dynamic and buckling analyses of structural components are performed by the differential quadrature method. To improve the accuracy of this method, an approach is proposed for selecting the sampling points which include base points and conditional points. The base points are taken as the roots of the Legendre polynomials. Accuracy of the problems analyzed will be increased by using the base points. The conditional points are determined according to boundary conditions and specified conditions of external load. A modified algorithm is proposed for applying two or more boundary conditions in a sampling point at boundary of domain, such that the higher-order partial differential equation can be solved without adding new sampling points. By applying this approach to variety problems, such as deflections of beam under nonuniformly distributed loading, vibration and buckling analyses of beam and plate, it is found that numerical results of the present approach are more accurate than those obtained by the equally-spaced differential quadrature method and is computationally efficient.

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